AGND and AVCC are the pins that supply power to the analog-to-digital convertor inside the ATmega chip. To get better analog performance, some circuit designs add extra filtering to this power supply so that digital noise from other parts of the system doesn't couple into the ADC circuitry.

AREF is the pin for the external analog reference voltage. This is used in some critical applications where a more accurate voltage reference is needed. When an analog input pin is at the same voltage as the AREF pin, the ADC will return 1023.